The present invention is directed to slab lenses developed from negative index of refraction materials (NIM) constructed from metal-dielectric composites and methods for their construction using frequency-selective photomodification.
Modern manufacturing techniques have led to significant developments in the capabilities of optical lenses and related imaging tools providing researchers and drug developers with insightful information about general features of various substances and materials. However, even today's most sophisticated lens is only capable of producing images with a limited spatial resolution, which means that the dimensions of observed objects can not be smaller than the half-wavelength of illuminating light This restriction (diffraction limit) is fundamental and cannot be avoided by traditional methods in standard microscopic optical systems, where an image of object is observed through a system of lenses. Current technology that allows the sub-wavelength optical resolution is based on near-field scanning optical microscope (NSOM). This technology does also have its own limitations, since NSOM uses nanoscale optical probes attached to a sophisticated positioning system and can only work in close proximity to the objects, at distances much smaller than the wavelength.
The refractive index is the most fundamental parameter to describe the interaction of electromagnetic radiation with matter. It is a complex number n=n′+in″ where n′ has generally been considered to be positive. While the condition n′<0 does not violate any fundamental physical law, materials with negative index have some unusual and counter-intuitive properties. For example, light, which is refracted at an interface between a positive and a negative index material, is bent in the “wrong” way with respect to the normal, group- and phase velocities are anti-parallel, wave- and Pointing vectors are anti-parallel, and the vectors {right arrow over (E)}, {right arrow over (H)}, and {right arrow over (k)} form a left-handed system. Because of these properties, such materials are synonymously called “left handed” or negative-index materials. Theoretical work on negative phase velocity dates back to Lamb (in hydrodynamics) [1] or Schuster (in optics) [2] and was considered in more detail by Mandel'shtam [3] and Veselago [4]. A historical survey referring to these and other early works has been set forth by Holloway et al. [5].
In general, left handed materials do not exist naturally, with some rare exceptions like bismuth that shows n′<0 at a wavelength of λ≈60 μm [6]. However, no naturally existing negative index material is known so far in the optical range of frequencies. Therefore, it is necessary to turn to man made, artificial materials which are composed in such a way that the averaged (effective) refractive index is less than zero: n′eff<0. Such a material can be obtained using photonic crystals (PC) [7-11]. However in this case, the interior structure of the material is not sub-wavelength. Consequently, PCs do not show the full range of possible benefits of left handed materials. For example, super-resolution, which has been predicted by Pendry [12], is not achievable with photonic band gap materials because their periodicity is in the range of the wavelength λ. A thin slab of a photonic crystal only restores small k-vector evanescent field components because the material can be considered as an effective medium only for long wavelengths, and large k-vector components are not restored [13-15]. A truly effective refractive index n′eff<0 can be achieved in metamaterials with structural dimensions far below the wavelength. Metamaterials for optical wavelengths must therefore be nano-crafted.
A possible—but not the only—approach to achieve a negative refractive index is to design a material where the (isotropic) permittivity ∈=∈′+i∈″ and the (isotropic) permeability μ=μ′+iμ″ obey the equation∈′|μ|+μ′|∈|<0.  (1)This leads to a negative real part of the refractive index n=√{square root over (∈μ)} [16]. Equation 1 is satisfied, if ∈′<0 and μ′<0. However, we note that this is not a necessary condition. There may be magnetically active media (i.e., μ≠1) with a positive real part μ′ for which Eq. 1 is fulfilled and which therefore show a negative n′.
Previously one has considered only isotropic media where ∈ and μ are complex scalar numbers. It has been shown that in the case of anisotropic media, where ∈ and μ are tensors, a negative refractive index is feasible even if the material shows no magnetic response (μ=1). If, for example, ∈⊥<0 and ∈∥>0, then n′<0 can be achieved [6, 17]. Despite the fact that using anisotropic media is a very promising approach, we will not focus on that topic here. This is mainly because so far a negative index for optical frequencies has only been achieved following the approach of magnetically active media.
The first recipe how to design a magnetically active material was suggested by Pendry in 1999 [18]: Two concentric split rings that face in opposite directions and that are of subwavelength dimensions were predicted to give rise to μ′<0. One can regard this as an electronic circuit consisting of inductive and capacitive elements. The rings form the inductances and the two slits as well as the gap between the two rings can be considered as capacitors. A magnetic field which is oriented perpendicular to the plane of drawing induces an opposing magnetic field in the loop due to Lenz's law. This leads to a diamagnetic response and hence to a negative real part of the permeability. The capacitors (the two slits and the gap between the rings) are necessary to assure that the wavelength of the resonance is larger than the dimensions of the split ring resonators (SRR).
Very soon after that theoretical prediction, Schultz and coworkers combined the SRR with a material that shows negative electric response in the 10 GHz range and consists of metallic wires in order to reduce the charge carrier density and hence shift the plasmonic response from optical frequencies down to GHz frequencies [19]. The outcome was the first-ever metamaterial with simultaneously negative real parts of the permeability and the permittivity [20] and consequently with a negative refractive index at approximately 10 GHz [21, 22]. From now on the race to push left handedness to higher frequencies was open. The GHz resonant SRRs had a diameter of several millimeters, but size reduction leads to a higher frequency response. The resonance frequency was pushed up to 1 THz using this scaling technique [23, 24].
An alternative to double SRRs is to fabricate only one SRR facing a metallic mirror and use it's mirror image as the second SRR [25]. The resonance frequency has been shifted to 50 THz using that technique. In order to increase the frequency even more, a simple further downscaling of the geometrical dimensions with wavelength becomes questionable because localized plasmonic effects must be considered. However, localized plasmons open a wide field of new design opportunities. For example, a double C-shaped SRR is not required any more. Originally, the double C-shaped structure was necessary in order to shift the resonance frequency to sufficiently low frequencies such that the requirement of sub wavelength dimension could be fulfilled. In the optical range, however, localized plasmons help to shift resonance frequencies to lower energies and consequently, the doubling of the split ring is not necessary at optical frequencies [26]. The first experimental proof that single SRRs show an electric response at 3.5 μm (85 THz) was given in 2004 by Linden and coworkers [27] and it was concluded that the magnetic response of single SRRs should be found at the same frequency. Meanwhile the electric resonance frequencies of single SRRs has even been pushed to the important telecom wavelength of 1.5 μm [28]. Other approaches of engineering metamaterials with magnetic activity that make use of localized plasmonic resonances, and abandon the classical split ring resonator shape completely, will be considered in the proposed work.
The “perfect” lens proposed by Pendry is among the most exciting applications regarding the NIMs, which have simultaneously negative real parts of permittivity ∈ and permeability μ. Pendry predicted that a slab with refractive index n=−1 surrounded by air allows the imaging of objects with sub-wavelength precision by recovering both propagating and evanescent waves. The NIM at optical frequencies demonstrated by the present inventors (“the Shalaev group”) recently paves the way in achieving the perfect lens in optics. However, commercially available optical NIMs are still far from the realization of a far-zone perfect lens because any realistic losses or impedance mismatch can eliminate the superlensing effect.
Provided that all of the dimensions of a system are much smaller than the wavelength, the electric and magnetic fields can be regarded as static and independent, and the requirement for superlensing of p-polarized waves (TM mode) is reduced to only ∈=−∈h, where ∈h is the permittivity of the host medium interfacing the lens. A slab of silver in air illuminated at its surface plasmon resonance (where λ=340 nm and ∈=−1) is a good candidate for such a NFSL. Experiments with silver slabs have already shown rapid growth of evanescent waves and imaging well beyond the diffraction limit. We note, however, that a NFSL can operate only at a single frequency ω satisfying the lens condition ∈′m(λop)=−∈h(λop) which is indeed a significant drawback of a lens based on bulk metals.
In sharp contrast to pure metal slabs, metal-dielectric composite films are characterized by an effective permittivity ∈θ that depends critically on the permittivities and the filling factors of both the metal and dielectric components. As a result, for a given host medium, ∈θ=∈θ(ω,p) may have the value of −∈h at practically any wavelength in the visible and NIR region. The wavelength corresponding to Rθ(∈θ)=−∈h depends on the structure of the composite and the material constants of the metal and dielectric components in the composite.